grandes-ecoles 2010 QIE1

grandes-ecoles · France · centrale-maths2__pc Groups Subgroup and Normal Subgroup Properties

In this question, the space $E$ has dimension $n = 3$. Let $(e _ { 1 } , e _ { 2 } , e _ { 3 })$ be an orthonormal basis of $E$ and $\mathcal { R } _ { 0 } = \left\{ e _ { i } - e _ { j } \mid 1 \leq i , j \leq 3 , i \neq j \right\}$.
Show that the vector subspace of $E$ spanned by the set $\mathcal { R } _ { 0 }$ is a vector plane.

In this question, the space $E$ has dimension $n = 3$. Let $(e _ { 1 } , e _ { 2 } , e _ { 3 })$ be an orthonormal basis of $E$ and $\mathcal { R } _ { 0 } = \left\{ e _ { i } - e _ { j } \mid 1 \leq i , j \leq 3 , i \neq j \right\}$.

Show that the vector subspace of $E$ spanned by the set $\mathcal { R } _ { 0 }$ is a vector plane.

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